"These proceedings are brought and are being used for political purposes and as such amount to an abuse of the process of this court," Workman said in his judgement at City of Westminster Magistrates' Court in London.
Ganic smiled and hugged his son and sobbing daughter as he was declared free to return to his home country.
The Serbian authorities immediately announced plans to appeal the decision, but Home Office officials said they believed the court judgement would allow the former Bosnian leader to leave the country.
Ganic intends to be back in Sarajevo on Wednesday, his family said.
In Bosnia, the Croat member of Bosnia's tripartite presidency Zeljko Komsic hailed the ruling as the "right decision".
"A politics of a 'Greater Serbia' has been inflicted another defeat, notably since all arguments of the Serb side were rejected and all arguments of defence accepted," a statement from Komsic's office said.
Serbia had claimed Ganic helped mastermind attacks on a Yugoslav army officers' club, on ambulances sent to the scene and later on an army convoy, causing the deaths of 40 Yugoslav soldiers at the start of the 1992-1995 Bosnian war.
Ganic's lawyers had argued throughout the six-day hearing that the man who was president of Bosnia from 1997-1999 was innocent and that the case was politically motivated.
That argument was supported by witnesses including Christian Schwarz-Schilling and Lord Paddy Ashdown, both former high representatives in Bosnia.
Ashdown also believed it was "no coincidence" that Ganic was arrested on the day that Bosnian Serb wartime leader Radovan Karadzic gave the opening speech in his genocide trial at a UN court, the judgement said.
However, Judge Workman believed this was likely to be "coincidence rather than design".